Apparatus and method for direct analysis of formation composition by magnetic resonance wireline logging

ABSTRACT

A wireline or logging while drilling device includes: a first coil configured to vary the intensity of a main magnetic field so as to produce phase modulation of signals emitted by spins in a sensitive volume; and a second coil configured to excite the spins in the sensitive volume in an inverse ratio of gyromagnetic constants of the spins; and receive signals from the spins displaced in frequency from the Larmor frequency of the spins by the phase modulation produced by the first coil.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of application Ser. No.14/874,835, filed Oct. 5, 2015, entitled “APPARATUS AND METHOD FORMEASURING VELOCITY AND COMPOSITION OF MATERIAL IN AND ADJACENT TO ABOREHOLE,” which claims priority to Provisional Application No.62/060,321, filed Oct. 6, 2014, entitled “APPARATUS AND METHOD FORMEASURING VELOCITY AND COMPOSITION OF MATERIAL IN AND ADJACENT TO ABOREHOLE,” the disclosures of all of which are incorporated by referenceherein in their entirety. Furthermore, this application claims priorityto Provisional Application No. 62/733,383, filed Sep. 19, 2018, entitled“APPARATUS AND METHOD FOR DIRECT ANALYSIS OF FORMATION COMPOSITION BYMAGNETIC RESONANCE WIRELINE LOGGING,” the disclosure of which isincorporated by reference herein in its entirety.

BACKGROUND OF THE INVENTION

This disclosure relates to the field of geological exploration, and inparticular to apparatus and methods for continuous analysis of signalsfrom magnetized geological formations by magnetic resonance wire linelogging.

Continuous analysis of moving magnetized material by magnetic resonancecreates periodic variation of the Larmor frequency of the movingmagnetized material by modulating coils that periodically vary the mainmagnetic B₀ field strength. This periodically varies the impedancepresented to the radio frequency oscillator power supply, whichimpedance function is a Lorentzian line. This methodology does notdirectly detect signals continuously emitted by the moving magnetizedmaterial.

Continuous creation and detection of signals emitted by movingmagnetized material is disclosed by U.S. Pat. No. 6,452,390B1 to Wollin,and by the application of this technology to flow in a boreholeenvironment disclosed in US 2016/0097664A1 to Wollin, both incorporatedherein by reference for all purposes.

SUMMARY

The systems, methods and devices of this disclosure each have severalinnovative aspects, no single one of which is solely responsible for thedesirable attributes disclosed herein.

In one embodiment described herein, a wireline or logging while drillingdevice includes: a first coil configured to vary the intensity of a mainmagnetic field so as to produce phase modulation of signals emitted byspins in a sensitive volume; and a second coil configured to excite thespins in the sensitive volume in an inverse ratio of gyromagneticconstants of the spins; and receive signals from the spins displaced infrequency from the Larmor frequency of the spins by the phase modulationproduced by the first coil

In another embodiment described herein, a flow measurement device formeasuring flow in or around a borehole of an earth formation includes: amagnet configured to generate a static solenoidal magnetic field with afield intensity that decreases in strength peripherally from the magnet;an electromagnet disposed around the magnet and configured to generate atime varying solenoidal magnetic field; and a radio frequency (RF) coildisposed around the magnet and configured to: generate an RF magneticfield transverse to the static solenoidal magnetic field to activatespins of nuclides having a same gyromagnetic ratio in a region ofinterest around the flow measurement device; and receive radiofrequencies corresponding to the gyromagnetic ratio.

This disclosure provides for, among other things, a device including apermanent magnet and coils that can identify producible hydrocarbonswith high special resolution. This disclosure also provides for, amongother things, a method for directly determining productive levels duringhydrocarbon wire line well logging. The method may include directdetection of a continuous signal from carbon 13 as a surrogate forhydrocarbon, enabled by continuous phase modulated dual resonanceexcitation of both hydrogen protons and carbon 13 atoms in a formationdeep to borehole effects, and may involve electronic and circuitrymodification of wire line logging tools. Logging speed can be adjustedto discriminate against non-producible surface-associated hydrocarbon,solid hydrocarbon, bitumin, and viscous high density hydrocarbon asthose compounds have short T2 spin spin dephasing. Thus, signalsreceived from carbon 13 atoms would be from producible hydrocarbon.

Analysis of the motion of an isolated spin, as described more completelybelow, yields an elliptic integral of the first kind which is notintegrable in closed form. However, look-up tables may be used toprovide the value of the integral for each value of the colatitude (flipangle) and each value of the periodic phase angle. The continuousreception of a signal with a known periodic phase angle phase modulatesthe emitted signal and provides the continuously detected continuouslyemitted signal with an extremely narrow bandwidth, markedly limitingJohnson-Nyquist noise, at known sideband frequencies displaced from theapplied B₁ radio frequency field permitting continuous detection of theemitted signal in the presence of the applied constant frequency B₁field by cross-correlation with those known frequencies.

The sine of the colatitude (“flip angle”) of the magnetization is thecoefficient of the detectable amplitude of the emitted signal. Inembodiments disclosed herein, this detectable amplitude is adjustable bythe amplitude of the applied radio frequency B₁ field, and by thelogging speed. The geometry of the applied radio frequency B₁ fielddefines the spatial resolution of the logging volume (vide infra).

The amplitude of the continuously received continuously emitted signalis a function of the quantity of magnetized material in the loggingvolume V (vide infra). The use of dual radio frequency coils permitsdetection of signal from low sensitivity low signal strength magnetizedmaterial by double resonance.

The logging tool can include a magnet configured to generate a staticsolenoidal magnetic field with a field intensity that decreases instrength peripherally from the magnet. The logging tool can include anelectromagnet disposed around the magnet and configured to generate asimilar but time varying solenoidal magnetic field. The logging tool caninclude one or more radio frequency (RF) coils disposed around themagnet. Dual RF coils can be configured to enable detection of signalsfrom low sensitivity low signal strength magnetized material by doubleresonance.

In some implementations, the logging tool can include a controllerconfigured to calculate the prevalence of selected nuclides in thelogging volume V (vide infra) around the logging tool based on thereceived signal. In some implementations, the volume of interest can bea region in or around a borehole in an earth formation.

Embodiments of the method disclosed can include inserting the magneticresonance logging tool into the borehole in the earth formation, thelogging tool comprising a magnet, an electromagnet disposed around themagnet, and radio frequency (RF) coils disposed around the magnet. Themethod can include generating, using the magnet, a static solenoidalmagnetic field, wherein the static solenoidal magnetic field has a fieldintensity that decreases in strength peripherally from the magnet. Themethod can include generating, using the electromagnet, a similar butweak time varying solenoidal magnetic field. The method can includegenerating, using the RF coils, an RF magnetic field transverse to thestatic solenoidal magnetic field and rotating at a Larmor radiofrequency corresponding to the solenoidal field intensity in the loggingvolume V (vide infra) around the logging tool. The method can includereceiving a signal induced in the RF coils by a magnetic field aroundthe RF coils.

In some implementations, the method can include calculating theprevalence of selected nuclides in the logging volume V (vide infra)around the logging tool based on the received signals.

Details of one or more implementations of the subject matter describedin this disclosure are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages will becomeapparent from the description, the drawings and the claims. Note thatthe relative dimensions of the following figures may not be drawn toscale.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B show a cross-sectional side view and top view of anexample embodiment of a magnetic resonance logging tool.

FIG. 2 shows a flow diagram of an example method for measuring a nuclideprevalence in or around a borehole in an earth formation.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

The following description is directed to certain implementations for thepurposes of describing the innovative aspects of this disclosure.However, a person having ordinary skill in the art will readilyrecognize that the teachings herein can be applied in a multitude ofdifferent ways. The described implementations may be implemented in anydevice, apparatus, or system that is capable of measuring nuclidecomposition of magnetized material.

The following disclosure pertains to measuring nuclide composition ofmaterial within a borehole or peripherally in a surrounding formation.The borehole may be present in an earth formation or a man-madestructure. The borehole may contain a logging tool employing nuclearspin or electron spin magnetic resonance for measurement. Applicationsof the logging tool disclosed herein include, without limitation,hydrocarbon production, hydraulic fracturing, groundwater migration,contaminant diffusion, or detecting formation migration or tectonicplate shift.

Transient response of spin systems have usually been described bysolutions to the Bloch equations which describes the magnetization as afunction of both the applied magnetic fields and the relaxation effectson a phenomenological basis. Solutions to the Bloch equations requireassumptions about the magnitude of these parameters and prescription ofboundary conditions, creating a differential system applicable to aparticular set of circumstances. To simplify this process further, thedescription below begins with the equation of motion of an isolatedspin, modeled as gyroscopic precession creating a magnetic moment whichinteracts with moments created by applied magnetic fields, thenintroduces the total magnetization as a function of spin density, andfinally limits the applicability of the equations so derived by therelationship between the times of the event sequence to the relaxationtimes. It is noted that non-producible hydrocarbons in general have muchshorter relaxation times than producible hydrocarbons. Short T2,non-producible hydrocarbons are solid or highly viscous with signalsthat extinguish rapidly. Signals from long T2, less viscous produciblehydrocarbons can be accentuated by adjusting logging speed. Formationpermeability can be demonstrated directly by observing flow rather thanempirically estimated.

A device (e.g. a wireline or logging while drilling device) can includeat least two coils. A first coil (e.g. the coil 102 shown in FIG. 1A andFIG. 1B) can be configured to slightly vary a main magnetic fieldproduced by a permanent magnet of the device, and a second coil (e.g.the coil 103 shown in FIG. 1A and FIG. 1B) can include at least one RFcoil configured to produce two RF fields of intensity in the inverseproportion of the gyromagnetic ratios of the excited spins in thesensitive volume of interest, and to receive signals from these spinsslightly displaced from the Larmor frequency of these spins by the phasemodulation produced by the first coil.

Gyroscopic Precession

A rigid body free in space without any constraints can rotatepermanently only about a principal axis of inertia”. If a rigid bodyrotates with speed ω₁ about a principal axis of inertia, and withω₂=ω₃=0 about the other two principal axes, then the angular momentumvector (i.e. moment of momentum vector) {right arrow over (M)} has thesame direction as the angular-speed vector {right arrow over (ω)}₁(which is along the axis of rotation). Angular velocities of a rigidbody about various axes in space, all intersecting in a point, can becompounded vectorially into a resultant angular speed about THE axis ofrotation.

We infer from the last statement that the resultant angular speed ω₁about THE axis of rotation taken as the resultant angular velocity Co′can be decomposed into a vector sum of angular velocities Σ{right arrowover (ω_(n))}. Further, taking the rigid body as having masssymmetrically distributed about all axes through the center of massyields a constant scalar moment of inertia I₀ about all axes, leading tothe desired result decomposing the angular momentum vector {right arrowover (M)}:

$\overset{\rightarrow}{M} = {{I_{0}\overset{\rightarrow}{\omega}} = {\sum\limits_{n}{I_{0}\overset{\rightarrow}{\omega_{n}}}}}$

From Newton's equations, with {right arrow over (M_(G))} being themoment of external forces about the center of mass:

$\overset{\rightarrow}{M_{G}} = {{\frac{d}{dt}I_{0}\overset{\rightarrow}{\omega}} = {\sum\limits_{n}{\frac{d}{dt}I_{0}{\overset{\rightarrow}{\omega_{n}}.}}}}$

Thus the vector sum of the moments of a set of external forces Σ{rightarrow over (M_(Gn))} equals the time rate of change of the total angularmomentum I₀{right arrow over (ω)}, i.e:

${\overset{\rightarrow}{M}}_{G} = {{\sum\limits_{n}\overset{\rightarrow}{M_{Gn}}} = {{\frac{d}{dt}I_{0}\overset{\rightarrow}{\omega}} = {\sum\limits_{n}{\frac{d}{dt}I_{0}{\overset{\rightarrow}{\omega_{n}}.}}}}}$

Gyromagnetic Ratio

Taking the rigid body as having a symmetrical distribution of chargeabout the center of mass creates a magnetic moment {right arrow over(μ)} about any axis of rotation proportional to the angular velocity{right arrow over (ω)} about that axis of rotation where each element ofcharge dq at distance r from the axis of rotation creates an elementd{right arrow over (μ)} of this magnetic moment {right arrow over (μ)}where, by definition of the magnetic moment,

${d\overset{\rightarrow}{\mu}} = {\left( {\pi \; r^{2}} \right)\left( {r\; \overset{\rightarrow}{\omega}} \right)\frac{dq}{2\pi \; r}}$

Each element of mass dw at distance r from this axis of rotation createsan element of the angular momentum (moment of momentum) dM of

d{right arrow over (M)}=(r)(r{right arrow over (ω)})dw.

The ratio is assumed to be a constant:

$\frac{d\overset{\rightarrow}{\mu}}{d\overset{\rightarrow}{M}} = {{\frac{1}{2}\left( \frac{dq}{dw} \right)} \equiv \gamma}$

γ being a scalar constant termed the gyromagnetic ratio. Integrating,with boundary condition {right arrow over (μ)}=0 when {right arrow over(M)}=0 yields:

{right arrow over (μ)}=γ{right arrow over (M)}.

General Equation of Motion of an Isolated Spin

A magnetic moment {right arrow over (μ)} subjected to a field ofmagnetic induction {right arrow over (B)} will experience a mechanicalmoment (torque) {right arrow over (M_(G))} such that:

{right arrow over (M _(G))}={right arrow over (μ)}33 {right arrow over(B)}

In free space of permeability μ₀, the magnetic induction {right arrowover (B)} is proportional to the magnetic field intensity {right arrowover (H)}:

{right arrow over (B)}=μ ₀ {right arrow over (H)}

Equating the rate of change of the angular momentum to the appliedmechanical moment (torque) yields

${\overset{\rightarrow}{\mu} \times \overset{\rightarrow}{B}} = {\frac{d}{dt}{\overset{\rightarrow}{M}.}}$

Multiplying by the gyromagnetic ratio γ and substituting {right arrowover (μ)}=γ{right arrow over (M)} and B=μ₀{right arrow over (H)} yields

${{\overset{\rightarrow}{\mu} \times \left( {\gamma\mu}_{0} \right)\overset{\rightarrow}{H}} = \frac{d}{dt}}{\overset{\rightarrow}{\mu}.}$

Defining γ′=γλ₀ yields the equation of motion of a magnetic moment(spin) subjected to a magnetic field intensity {right arrow over (H)}:

${\overset{\rightarrow}{\mu} \times y^{\prime}\overset{\rightarrow}{H}} = {\frac{d}{dt}{\overset{\rightarrow}{\mu}.}}$

Dividing by μ yields the instantaneous angular velocity of a magneticmoment (spin) {right arrow over (μ)} subjected to a time varying ambientmagnetic field intensity {right arrow over (H)}:

${{{\overset{\rightarrow}{I}}_{\mu} \times y^{\prime}\overset{\rightarrow}{H}} = {\frac{d}{dt}{\overset{\rightarrow}{I}}_{\mu}}},$

which is a linear differential equation with constant coefficients,allowing superposition.Decomposing {right arrow over (H)} into H₀, h_(p), and h_(n)

Define an orthogonal coordinate system for {right arrow over (I)}_(μ),and {right arrow over (H)} as {right arrow over (z)}, {right arrow over(x)}, j{right arrow over (y)} where {right arrow over (x)}+j{right arrowover (y)} forms Gaussian planes everywhere orthogonal to {right arrowover (z)}. This allows decomposition of the ambient magnetic fieldintensity {right arrow over (H)} such that:

{right arrow over (H)}=[H ₀ +h _(p) cos(Ωt)]{right arrow over(z)}+{right arrow over (h _(n))}e ^(jγ′H) ⁰ ^(t),

where H₀ is a strong non-time variant ambient magnetic field intensity,h_(p) is co-aligned with H₀ and sinusoidally periodic at frequency Ω,and h_(n) is everywheres orthogonal to H₀ rotating in the localorthogonal {right arrow over (x)},j{right arrow over (y)} Gaussian planeat angular velocity γμ₀H₀=γB₀=ω₀, which is the Larmor frequency.

Equation of Motion

Substituting and rearranging in differential form

d{right arrow over (I)} _(μ)=({right arrow over (I)} _(μ) ×γ′H ₀ {rightarrow over (z)})dt+({right arrow over (I)} _(μ)×[γ′h _(p) cos(Ωt)]{rightarrow over (z)})dt+({right arrow over (I)} _(μ)Δγ′{right arrow over (h_(n))}e ^(jγ′H) ⁰ ^(t))dt

since the vector product (cross product) distributes across a vectorsum.

The first term creates a constant precession of {right arrow over(I)}_(μ) of angular velocity γ′H₀ about the {right arrow over (z)} axis.

The second term creates a periodic precession of {right arrow over(I)}_(μ) of peak angular velocity γ′h_(p) and temporal frequency Ω aboutthe {right arrow over (z)} axis.

The third term represents a precession of {right arrow over (I)}_(μ) ofangular velocity γ′h_(n) about an axis perpendicular to the {right arrowover (z)} axis, said axis rotating with angular velocity γ′H₀ in the{right arrow over (x)}+j{right arrow over (y)} Gaussian plane, aperiodic Bloch-Siegert effect.

These three instantaneous angular velocities add vectorially to aresultant angular velocity, which when integrated over time, creates thelocus of {right arrow over (I)}_(μ) in space.

If γ′h_(n)<<γ′h_(p)<<γ′H₀, the locus of the unit vector {right arrowover (I)}_(μ) describes a serpiginous line of colatitude θ and longitudeφ on a unit diameter sphere, said sphere rotating with an angularvelocity γ′H₀ in the local {right arrow over (x)}+j{right arrow over(y)} Gaussian plane. The rate of increase of θ is maximum at the poles(θ=0, π) and decreases at mid-latitude to 0.340 of maximum at theequator (θ=π/2). The governing equations are:

${{\overset{\rightarrow}{1}}_{u}X\; \gamma^{\prime}\overset{\rightarrow}{h_{n}^{\prime}}}\overset{\Delta}{=}{{\overset{\rightarrow}{\omega}}_{n} = {\frac{d\; \overset{\rightarrow}{\theta}}{dt} = {{{\overset{\rightarrow}{1}}_{u}\left\lbrack {{\cos^{2}\theta} + {\sin^{2}{\theta cos}^{2}\phi}} \right\rbrack}^{\frac{1}{2}}X\; \gamma^{\prime}{\overset{\rightarrow}{h}}_{n}}}}$${{\overset{\rightarrow}{1}}_{u}X\; \gamma^{\prime}\overset{\rightarrow}{h_{p}}\cos \; \Omega \; t} = {{\overset{\rightarrow}{\omega}}_{p} = {\frac{d\; \overset{\rightarrow}{\phi}}{dt} = {\overset{\rightarrow}{z}\gamma^{\prime}h_{p}\cos \; \Omega \; t}}}$${{\overset{\rightarrow}{\phi} = {{\int{{\overset{\rightarrow}{\omega}}_{p}{dt}}} = {\frac{y^{\prime}}{\Omega}\sin \; \Omega \; t}}};{\frac{\gamma^{\prime}h_{p}}{\Omega} \cong 1.8}},{{{to}\mspace{14mu} {maximize}\mspace{14mu} {{J_{1}\left( {{vide}\mspace{14mu} {infra}} \right)}.h_{n}^{\prime}}}\overset{\Delta}{=}{h_{n}\left\lbrack {{\cos^{2}\theta} + {\left( {\sin^{2}\theta} \right)\left\lbrack {\cos^{2}\left( {\frac{\gamma^{\prime}h_{p}}{\Omega}\sin \; \Omega \; t} \right)} \right\rbrack}} \right\rbrack}^{\frac{1}{2}}}$As  θ → (0, π); h_(n)^(′) → h_(n)${\gamma^{\prime}h_{n}^{\prime}}\overset{\Delta}{=}{{\gamma^{\prime}{{h_{n}\left\lbrack {1 - {\sin^{2}{\theta \left\lbrack {1 - {\cos^{2}\left( {\frac{\gamma^{\prime}h_{p}}{\Omega}\sin \; \Omega \; t} \right)}} \right\rbrack}}} \right\rbrack}^{\frac{1}{2}}.\frac{d\; \theta}{dt}}} = {\gamma^{\prime}{h_{n}\left\lbrack {1 - {\sin^{2}{{\theta sin}^{2}\left( {\frac{\gamma \; h_{p}}{\Omega}\sin \; \Omega \; t} \right)}}} \right\rbrack}^{\frac{1}{2}}}}$${\int_{0}^{\tau}{\gamma^{\prime}h_{n}{dt}}} = {\int_{0}^{\theta}{\left\lbrack {1 - {\sin^{2}{{\theta sin}^{2}\left( {\frac{\gamma^{\prime}h_{p}}{\Omega}\sin \; \Omega \; t} \right)}}} \right\rbrack^{- \frac{1}{2}}d\; \theta}}$${\gamma^{\prime}h_{n}\tau} = {\int_{0}^{\theta}{\left\lbrack {1 - {\sin^{2}\theta \; \sin^{2}\phi}} \right\rbrack^{- \frac{1}{2}}d\; \theta}}$${\gamma^{\prime}h_{n}\tau}\overset{\Delta}{=}{F\left( {\theta \backslash \phi} \right)}$

which is an incomplete elliptic integral of the first kind with aperiodic modular angle, and is not integrable.

Output Voltage in Receiver Coil

Based on the foregoing, continuous analysis of signals from magnetizedmaterials may be achieved. The continuous reception of a signal with aperiodic frequency phase modulates the continuously emitted signal andprovides the continuously detected continuously emitted signal with anextremely narrow bandwidth, markedly limiting Johnson-Nyquist noise, atknown sideband frequencies displaced from the applied B₁ radio frequencyfield permitting continuous detection of the emitted signal in thepresence of the applied constant frequency B₁ field.

The sine of the colatitude (“flip angle”) of the magnetization is thecoefficient of the detectable amplitude of the emitted signal. Thisdetectable amplitude is adjustable by the amplitude of the applied radiofrequency B₁ field, which detectable amplitude becomes a function of theknown logging speed and of the unknown prevalence of the magnetizednuclide in the logging volume V (vide infra).

The amplitude of the continuously received continuously emitted signalis a function of the quantity of magnetized material in the loggingvolume V (vide infra). The use of dual radio frequency coils permitsdetection of signal from low signal strength low sensitivity magnetizedmaterial utilizing the Hartmann-Hahn ratio. Applying double resonancefrequencies h_(n) ₁ and h_(n) ₂ to nuclides of gyromagnetic ratio γ₁ andγ₂ respectively in the same logging volume V (vide infra) during loggingvolume dwell time t with the condition of maximum energy transfer fromh_(n) ₁ and h_(n) ₂ to the output signal (vide infra) γ₁h_(n) ₁t=γ₂h_(n) ₂ t=π leads directly to the Hahn-Hartman ratio

$\frac{\gamma_{1}}{\gamma_{2}} = {\frac{h_{n_{2}}}{h_{n_{1}}}.}$

This is explained further as follows:

If the transverse magnetization {right arrow over (μ)}_(T) is defined asthe projection of the magnetic moment {right arrow over (μ)} on the{right arrow over (x)}+j{right arrow over (y)} Gaussian plane, whichplane is transverse to the {right arrow over (z)} axis, such that:

{right arrow over (μ)}_(T)=({right arrow over (μ)} sin θ)e ^(jφ),

where θ is the colatitude of {right arrow over (μ)} with respect to the{right arrow over (z)} axis, and φ is the longitude taken from a zeromeridian through the {right arrow over (z)} and j{right arrow over (y)}axes, the instantaneous angular velocity of {right arrow over (u)}_(T)in the {right arrow over (x)}+j{right arrow over (y)} Gaussian planethen is:

{right arrow over (ω)}_(T)=(γ′h _(p) cos(Ωt)+γ′H ₀){right arrow over(z)}

creating a phase incrementation φ of {right arrow over (μ)}_(T) at timet of

$\overset{\rightarrow}{\phi} = {{\int_{0}^{t}{{\overset{\rightarrow}{\omega}}_{T}{dt}}} = {\left( {{\frac{\gamma^{\prime}h_{p}}{\Omega}{\sin \left( {\Omega \; t} \right)}} + {\gamma^{\prime}H_{0}t}} \right){\overset{\rightarrow}{z}.}}}$

A coil of N turns will subtend the rotating magnetization of {rightarrow over (μ_(T))} such that:

$\mu_{c} = {{{\mu sin}\; {\theta \left( {\sin \; \phi} \right)}} = {\left( {\mu \; \sin \; \theta} \right){{\sin \left\lbrack {{\frac{\gamma^{\prime}h_{p}}{\Omega}{\sin \left( {\Omega \; t} \right)}} + {\gamma^{\prime}H_{0}t}} \right\rbrack}.}}}$

By Faraday's law, the voltage induced in the coil is

$V_{c} = {{N\; \mu_{0}\frac{d\; \mu_{c}}{dt}} = {N\; {\mu_{0}\left( {{\left( {\mu \; \sin \; \theta} \right)\left( {{\gamma^{\prime}h_{p}\cos \; \left( {\Omega \; t} \right)} + {\gamma^{\prime}H_{0}}} \right)\left( {\cos \left\lbrack {{\frac{\gamma^{\prime}h_{p}}{\Omega}{\sin \left( {\Omega \; t} \right)}} + {\gamma^{\prime}H_{0}t}} \right\rbrack} \right)} + {{\sin \left\lbrack {\frac{\gamma^{\prime}h_{p}}{\Omega}{\sin \left( {{\Omega \; t} + {\gamma^{\prime}H_{0}t}} \right)}} \right\rbrack}\left( {\mu \; \cos \; \theta} \right)\left( \frac{d\; \theta}{dt} \right)}} \right)}}}$$\mspace{20mu} {{{Since}\frac{d\; \theta}{dt}} \leq {\gamma^{\prime}h_{n}}{\gamma^{\prime}h_{p}}{\gamma^{\prime}H_{0}\text{:}}}$$\mspace{20mu} {{V_{c} \cong {{N\left( {\mu_{0}\mu \; \sin \; \theta} \right)}\left( {\gamma^{\prime}H_{0}} \right)\left( {\cos \left\lbrack {{\frac{\gamma^{\prime}h_{p}}{\Omega}{\sin \left( {\Omega \; t} \right)}} + {\gamma^{\prime}H_{0}t}} \right\rbrack} \right)}},}$

where N is the number of turns in the coil, μ₀ is the permeability offree space, H₀ is the main magnetic field intensity, γ′ is thegyromagnetic ratio μ₀γ, h_(p) is the peak magnetic field intensity ofthe phase modulating field of temporal frequency Ω, and θ is thecolatitude of the magnetic moment (spin) of magnetic field intensity μ.

The Fourier transform of V_(c) with respect to time is

${\left. {V_{c}} \right|_{\omega} = {\pi \; A{\sum\limits_{n = {- \infty}}^{+ \infty}\left\lbrack {{{J_{n}\left( \frac{\gamma^{\prime}h_{p}}{\Omega} \right)}\delta_{\lbrack{\omega - {({{\gamma^{\prime}H_{0}} + {n\; \Omega}})}}\rbrack}} + {{J_{n}\left( \frac{\gamma^{\prime}h_{p}}{\Omega} \right)}\delta_{\lbrack{\omega + {({{\gamma^{\prime}H_{0}} + {n\; \Omega}})}}\rbrack}}} \right\rbrack}}},\mspace{20mu} {{{where}\mspace{14mu} A} = {{N\left( {\mu_{0}\mu} \right)}\left( {\mu_{0}H_{0}} \right)\gamma \; \sin \; {\theta.}}}$

Phase Modulating Field

Three voltages are induced in the receiver coil; the first by h_(p) at alow frequency Ω, the second by h_(n) of radio frequency (RF) frequencyγ′H₀=γμ₀H₀=γB₀=ω₀, and the third by the precession of the magneticmoment {right arrow over (μ)} (spin) consisting of a central frequencyω₀ with an infinite number of sidebands spaced about this central RFLarmor frequency ω₀ at frequency intervals Ω. These sidebands permitadjustment of h_(n) for the maximum output voltage in the receiver coilsince they can be detected in the presence of the applied Larmor RFfrequency ω₀ and the applied phase modulating low frequency Ω byrejecting these latter frequencies with circuit filters or lock-inamplifiers and/or by detection, heterodyning, and homodyne demodulationtechniques employed in prior art radio receivers. The preferred firstsideband voltage is maximized if the argument of the first sideband isadjusted so that:

${J_{1}\left( \frac{\gamma^{\prime}h_{p}}{\Omega} \right)} \cong {J_{1}(1.8)} \cong {0.582\left( {{Abramowitz},{{op}.\mspace{14mu} {cit}.\mspace{14mu} p.\mspace{14mu} 390}} \right)}$

yielding

${\Omega = {\frac{\gamma^{\prime}h_{p}}{1.8} = {\frac{{\gamma\mu}_{0}h_{p}}{1.8} = {\frac{\gamma \; b_{p}}{1.8} = {\frac{2{\pi \left( {42.589 \times 10^{6}} \right)}}{1.8} \cdot b_{p}}}}}},$

then the side band frequency f_(p)≅23.6×10⁶·b_(p) where 2πf_(p)=Ω. Thepeak excursion of the magnetic moment (spin) from the plane containingH₀ and orthogonal to h_(n) is ±1.8 radians, or ±103 degrees.

Thus, Ω and h_(p) are so defined but are independent of the mainmagnetic field strength H₀ or Larmor frequency γ′H₀=γμ₀H=γB₀=ω₀.

WireLine Logging Application

If the magnetic moments (spins) {right arrow over (μ)} dwell in a spacecontaining H₀ and h_(p) for a time sufficient to create significantmagnetic field intensity (Slichter, op. cit. Ch.2.11, p. 51) and thendwell in a space additionally containing h_(n) for a dwell time suchthat nutation occurs through an angle θ=π, maximum energy is absorbed bythe magnetic moments (spins) {right arrow over (μ)} from h_(n).

A medium (lattice) containing a distribution of magnetic moments {rightarrow over (μ)}(spins) of dwell time t in a space in which thesemagnetic moments are subjected to both a strong static magnetic fieldintensity {right arrow over (H₀)} and co-aligned weak component h_(p),sinusoidally varying with a frequency Ω, will absorb energy from themagnetic moments by first order kinetics, opposed by random thermalmotion, creating a magnetic field intensity {right arrow over (m)} suchthat

{right arrow over ({circumflex over (m)})}{right arrow over ({circumflexover (X)})}({right arrow over (H)} ₀ +{right arrow over (h)} _(p) cosΩt)(1−e ^(−t/T) ¹ ),

(where

denotes both spatial vector and temporal phasor), {right arrow over({circumflex over (X)})} being the complex susceptibility, T₁ thespin-lattice relaxation.

The logging volume V is the space occupied by the magnetic fields H₀,h_(p), and h_(n), as all previously defined. If the spins occupy thevolume V for the time τ the volume logging rate is V/τ. After a time τthe spins in the logging volume are at colatitude (“flip” angle) θ andphase angle φ as governed by γ′h_(n)τ=F(θ†φ). Then

$\frac{V}{\tau} = {\gamma^{\prime}\frac{h_{n}}{F\left( {\theta \backslash \phi} \right)}V}$

The detectable transverse magnetization is M=∫₀ ^(θ) m sin θ dθ,M=(1−cos θ). For maximum M,

${\frac{dM}{d\; \theta} = {{m\; \sin \; \theta} = 0}};{\theta = {{n\; {\pi.\mspace{14mu} {F\left( {\pi \backslash \phi} \right)}}} = {{2{F\left( {{\pi/2}\backslash \phi} \right)}} = {2K}}}}$

K is a complete elliptic integral of the first kind. φ is the modularangle. φ is periodic,

$\phi = \frac{\gamma \; h_{p}}{\Omega}$

sin Ωt, a formulation not treated elsewhere.

$\mspace{20mu} {K\overset{\Delta}{=}{\int_{0}^{\pi/2}{\left\lbrack {1 - {\left( {\sin^{2}\phi} \right)\left( {\sin^{2}\theta} \right)}} \right\rbrack^{{- 1}/2}d\; \theta}}}$$\mspace{20mu} {{{{if}\mspace{14mu} \frac{d\; \theta}{dt}}\Omega},{{{{then}\frac{d\; \theta}{d\; \phi}} \cong {{o.\mspace{14mu} \sin^{2}}\phi}} = {{1 - {\cos^{2}\phi}}\overset{\Delta}{=}{{{m.\cos}\; \phi}\overset{m}{=}{{\frac{1}{2\pi}{\int_{- \pi}^{+ \pi}{{\cos \left( {\frac{\gamma \; h_{p}}{\Omega}\sin \; \Omega \; t} \right)}{d\left( {\Omega \; t} \right)}}}} = {\frac{1}{\pi}{\int_{0}^{\pi}{{\cos \left( {\frac{\gamma \; h_{p}}{\Omega}\sin \; \Omega \; t} \right)}{d\left( {\Omega \; t} \right)}}}}}}}}}$$\mspace{20mu} {{{{But}\mspace{14mu} {J_{n}(z)}} = {\frac{1}{\pi}{\int_{0}^{\pi}{{\cos \left( {{z\; \sin \; \phi} - {n\; \phi}} \right)}d\; \phi}}}};({Bessel})}\mspace{20mu}$$\mspace{20mu} {{{J_{0}\left( \frac{\gamma \; h_{p}}{\Omega} \right)} = {\frac{1}{\pi}{\int_{0}^{\pi}{{\cos \left( {\frac{\gamma \; h_{p}}{\Omega}\ \sin \; \Omega \; t} \right)}{d\left( {\Omega \; t} \right)}\mspace{20mu} {m = {{1 - {J_{0}^{2}(1.8)}} = {{1 - ({.340})^{2}} = {.884}}}}}}}};}$$\mspace{20mu} {K = {{\int_{0}^{\pi/2}{\left\lbrack {1 - {{.884}\sin^{2}\theta}} \right\rbrack^{{- 1}/2}d\; \theta}} = {{2.5\mspace{20mu} {V/\tau}} = {{\left\lbrack \frac{\gamma^{\prime}}{2(2.5)} \right\rbrack {Vh}_{n}} = {{\left\lbrack \frac{\gamma}{2(2.5)} \right\rbrack {Vb}_{n}} = {{\left\lbrack \frac{2{\pi \left( {42.6 \times 10^{6}} \right)}}{2(2.5)} \right\rbrack {Vb}_{n}\mspace{14mu} {Tesla}\mspace{20mu} {V/\tau}} = {{53.5 \times 10^{6}{Vb}_{n}\mspace{14mu} {Tesla}} = {535 \times 10^{9}{Vb}_{n}\mspace{14mu} {Gauss}}}}}}}}}$

Exemplary Magnetic Resonance Well Logging Tool

With this background, a logging tool implementing these principles canbe designed.

FIGS. 1A and 1B show a cross-sectional side view and top view,respectively, of an example embodiment of a magnetic resonance welllogging tool 100. The tool 100 includes a magnet 101 having north andsouth poles, an electromagnet 102, and radio frequency (“RF”) coils 103and 104. The tool 100 is configured to insert into a borehole 105 of anearth formation 106 suspended by a wireline and withdrawn creatingrelative motion between the tool and the formation.

The tool 100 can include a magnet 101. The magnet 101 can generate astatic magnetic field around the flow measurement device 100 that isgenerally solenoidal in shape. The strength of the static magnetic fieldgenerated by magnet 101 can decrease in strength peripherally from themagnet. The magnet 101 can be a permanent magnet. The magnet 101 can beof any size or shape appropriate to the dimensions of the borehole andthe measurement application for which it will be used, including a longcylindrical shape.

The logging tool 100 can include an electromagnet 102. The electromagnet102 can be configured to generate a time varying magnetic field aroundthe tool 100 that is generally solenoidal in shape. The electromagnet102 can be of any type suitable for generating a solenoidal magneticfield of roughly the same relative distribution as the static magneticfield. The electromagnet 102 can take the shape of a helical coilsurrounding the magnet 101. The strength of the time varying magneticfield generated by the electromagnet 102 can vary linearly with theapplication of a time varying current through the electromagnet 102. Thestrength of the time varying magnetic field generated by theelectromagnet 102 can be relatively weak compared to the strength of thestatic magnetic field; for example, a fraction of a Gauss to severalGauss compared to several thousand Gauss in the static magnetic field.The frequency of the time varying magnetic field generated by theelectromagnet 102 can be very low compared to the frequency of the RFmagnetic field generated by the RF coils 103 and 104.

The tool 100 can include radio frequency (“RF”) coils 103 and 104. TheRF coils can be configured to continuously generate a time varyingmagnetic field h_(n) transverse to the H₀ static solenoidal magneticfield generated by the magnet 101. The RF coils 103 and 104 can be asingle coil or made up of multiple coils. The RF coils 103 and 104 canbe a single coil configured to continuously both create and receivesignals from time varying magnetic fields. Alternatively, separate RFcoils 103 and 104 can be employed continuously as a transmit coil and areceiving coil, respectively. The RF coils 103 and 104 can be of abirdcage or quadrature design, or any other coil, cage, or antennastructure suitable for directing an RF magnetic field outward from thetool 100. In one embodiment, the RF coils 103 and 104 comprise atransmitting birdcage coil disposed around the magnet and configured tocontinuously generate the RF magnetic field, and a receiving birdcagecoil disposed around the magnet and configured to continuously outputthe received signal. In another embodiment, the RF coils 103 and 104could comprise a first birdcage coil disposed around the magnet andconfigured to operate at a first frequency, and a second birdcage coildisposed around the magnet and configured to operate at a secondfrequency. The RF coils 103 and 104 can be tuned to resonate at thedesired frequency of operation. The RF coils 103 and 104 can have a highquality factor (“Q”) for improved efficiency of transmission and receiptof time varying magnetic fields. The RF coils 103 and 104 generate atime varying h_(n) magnetic field rotating at the Larmor frequencies ofthe selected nuclides (e.g. H1 and C13), ω₀=γh₀ corresponding to the H₀static solenoidal magnetic field intensity h₀ in the logging volume Varound the logging tool 100 in the ratio of the gyromagnetic constantsof the selected nuclides. The logging volume V can take the shape of asegment of a barrel shaped prolate or oblate ellipsoidal surface havinga finite thickness generated about the centerline of the logging tool100. The RF coils 103 and 104 can be configured to output receivedsignals induced by the magnetic fields about the RF coils 103 and 104.

Multiple RF coils 103 and 104 can be employed to measure the relativeabundance of two different nuclides in the logging volume V; forexample, detection and measurement of both ¹H and ¹³C by the same tool100 in the same logging volume V. Exciting RF coils 103 and 104 withfrequencies selected for two different nuclides permits implementationof double resonance yielding the prevalence of, e. g., ¹H and ¹³C,thereby implementing a multiphase “cut meter” or wireline loggingmodality. Such a system may be valuable, for example, for measuring therelative abundance of hydrocarbons versus brine in the logging volume Vsurrounding the tool. Such information can be valuable when searchingfor, e.g. hydrocarbon deposits.

In operation, the magnet 101 and electromagnet 102 can create a strongsolenoidal field with a very weak slowly time varying component in theborehole 105 and in the surrounding invaded and non-invaded earthformation 106 beneath any mudcake. The RF coils 103 and 104 can createan adjustable RF magnetic field essentially orthogonal to the solenoidalfield. The RF magnetic fields rotate at the Larmor frequency and causesthe spins to nutate with increasing colatitude angle with respect to thestrong magnetic field, permitting reception of signal induced by amagnetic field created by the nutating spins at sideband frequenciesdisplaced from the applied Larmor frequencies. Selecting the Larmorfrequency selects the depth of investigation, where the depth ofinvestigation represents the distance from the tool 100 to the region ofinterest of spin activation about the logging tool. That is, for a givenstrength of the static solenoidal magnetic field H₀, adjusting thefrequency of the RF magnetic field generated by the RF coils 103 and 104controls at what distance from the tool 100 spins of the samegyromagnetic ratio will be affected. An RF magnetic field having ahigher frequency will activate spins of the same gyromagnetic ratiorelatively closer to the logging tool 100, and an RF magnetic fieldhaving a lower frequency will activate spins of the same gyromagneticratio relatively further from the tool 100. The strength of the slowlyvarying component of the solenoidal field is adjusted for optimum signalreception of the preferably first sideband frequencies from the depth ofinvestigation.

The conditions generated by the tool 100 create both nutation, withincreasing co-latitude (flip angle), and periodic phase modulation ofthe rotational Larmor frequency of the spins. The received signal theninduced in the RF coils 103 and 104 is sinusoidal with slowly varyingfrequency whose Fourier transform yields a central Larmor frequency anddiscrete side bands displaced by the phase modulation frequency. Theseside bands can then be detected in the presence of the strong continuousapplied Larmor excitation frequency field by means known in the artincluding heterodyne frequency shift, homodyne detection, and crosscorrelation in a lock-in amplifier. Adjusting the strength of theapplied Larmor excitation frequency field B₁ for maximum receivedsignals yield a function of the prevalence of the spins and of thelogging speed of the selected nuclides at the depth of investigation inthe logging volume V.

The radio frequencies supplied to each coil 103 and 104 are in thefrequency ratio of the gyromagnetic ratios of the detected nuclides toexcite the same logging volume. These frequencies can be chosen so thatthe logging volume so selected is peripheral to borehole effects. Theamplitude of each supplied radio frequency is inversely proportional tothe gyromagnetic ratios of the detected nuclides to permit crossexcitation of the less prevalent by the more prevalent nuclide by anappropriate resonance technique (the Hahn-Hartmann effect is anon-limiting example of such a technique). The amplitudes of thesesupplied radio frequencies are adjusted to produce maximum signal toaccount for variations in logging speed. The current in electromagnet102 can be adjusted to maximize the value of the preferably first sideband about the Larmor frequencies from the received signals induced inthe RF coils 103 and 104.

FIG. 2 shows a flow diagram of an example method for measuringprevalence of selected nuclides in or around a borehole in an earthformation, using the techniques described above. In block 310, a tool ordevice (e.g. a wireline or logging while drilling device describedherein) is inserted into a borehole. In block 320, the device generatesa static solenoidal magnetic field. In block 330, the device generates atime varying solenoidal magnetic field. In block 340, the devicegenerates an RF magnetic field transverse to the solenoidal magneticfield. This field may, for example, excite spins in a sensitive volumein an inverse ratio of gyromagnetic constants (e.g. gyromagnetic ratios)of the spins. In block 350, the device may measure a received signalinduced in an RF coil of the device. The received signal may be, forexample, from the spins, and may be displaced in frequency from theLarmor frequency of the spins by the phase modulation produced by the RFcoil. The received signal may, for example, have a radio frequencycorresponding to the gyromagnetic ratio.

The foregoing disclosure is equally applicable to nuclear and electronmagnetic resonance. Furthermore, the measurement of prevalence ofnuclides by the device described in this disclosure is applicable notonly to liquid or gas, but to other materials, such as mixtures,slurries, aggregates, blowing particles, viscous plastics as well as tosolid materials.

Preferred embodiments of the invention have now been described. It willbe appreciated by those skilled in the art that such embodiments areintended to exemplify the invention. Various other embodiments of theinvention will be apparent, which fall within the spirit and scope ofthe invention.

What is claimed is:
 1. A wireline or logging while drilling device,comprising: a first coil configured to vary the intensity of a mainmagnetic field so as to produce phase modulation of signals emitted byspins in a sensitive volume; and a second coil configured to: excite thespins in the sensitive volume in an inverse ratio of gyromagneticconstants of the spins; and receive signals from the spins displaced infrequency from the Larmor frequency of the spins by the phase modulationproduced by the first coil.
 2. A flow measurement device for measuringflow in or around a borehole of an earth formation, comprising: a magnetconfigured to generate a static solenoidal magnetic field with a fieldintensity that decreases in strength peripherally from the magnet; anelectromagnet disposed around the magnet and configured to generate atime varying solenoidal magnetic field; and a radio frequency (RF) coildisposed around the magnet and configured to: generate an RF magneticfield transverse to the static solenoidal magnetic field to activatespins of nuclides having a same gyromagnetic ratio in a region ofinterest around the flow measurement device; and receive radiofrequencies corresponding to the gyromagnetic ratio.
 3. The flowmeasurement device of claim 2, wherein the RF coil is configured toreceive frequencies in the frequency ratio of the gyromagnetic ratio. 4.The flow measurement device of claim 2, wherein the RF coil isconfigured to receive a frequency having an amplitude that is inverselyproportional to the gyromagnetic ratio.
 5. The flow measurement deviceof claim 2, wherein the RF coil is configured to activate spins of afirst nuclide and a second nuclide having the same gyromagnetic ratio.